Install nginx

For Ubuntu, run aptitude install nginx. For other distros, run the corresponding package manager, or see http://wiki.nginx.org/Install.

Install PHP FastCGI

For Ubuntu, read this excellent page on how to configure PHP and FastCGI for nginx.

For Gentoo, PHP will run as a FastCGI service (fpm), so the nginx server will run PHP as a separated process:

The default settings of php-fpm are good for most servers. For special configurations, visit the PHP FPM site.

Configure Nginx

nginx configuration files reside in:

/etc/nginx/sites-available/ on Ubuntu (for sites running on that nginx instance)
/etc/nginx/nginx.conf on Gentoo and Raspbian(= Debian optimized for Raspberry Pi)
Here is an sample nginx configuration file, joomla.conf, that you can reuse over all your nginx enabled-sites.

server {
        listen 80;
        server_name YOUR_DOMAIN;
        server_name_in_redirect off;

        access_log /var/log/nginx/localhost.access_log;
        error_log /var/log/nginx/localhost.error_log info;

        root PATH_ON_SERVER;
        index index.php index.html index.htm default.html default.htm;
        # Support Clean (aka Search Engine Friendly) URLs
        location / {
                try_files $uri $uri/ /index.php?$args;
        }

        # deny running scripts inside writable directories
        location ~* /(images|cache|media|logs|tmp)/.*\.(php|pl|py|jsp|asp|sh|cgi)$ {
                return 403;
                error_page 403 /403_error.html;
        }

        location ~ \.php$ {
            fastcgi_pass  127.0.0.1:9000;
            fastcgi_index index.php;
            include fastcgi_params;
            fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;
            include /etc/nginx/fastcgi.conf;
        }

        # caching of files 
        location ~* \.(ico|pdf|flv)$ {
                expires 1y;
        }

        location ~* \.(js|css|png|jpg|jpeg|gif|swf|xml|txt)$ {
                expires 14d;
        }

}

Pay attention to a few things:

1. The parameter fastcgi_pass is set to 127.0.0.1:9000, corresponding to the port that fpm is configured to listen to. This means you can run the PHP processes on separate servers. On Gentoo, you can find this configuration in /etc/php/fpm-php5.3/php-fpm.conf/
2. Don't forget to replace YOUR_DOMAIN & PATH_ON_SERVER above depending on your domain and the path of Joomla on your server.

GZip support

If you need GZip compression support, add the following section to the http section of the main nginx configuration file:

        gzip on;
        gzip_http_version 1.1;
        gzip_comp_level 6;
        gzip_min_length 1100;
        gzip_buffers 4 8k;
        gzip_types text/plain application/xhtml+xml text/css application/xml application/xml+rss text/javascript application/javascript application/x-javascript
        gzip_proxied     any;
        gzip_disable     "MSIE [1-6]\.";